Yes.

If a simple graph G is connected and the degree of every vertex of G is a positive even integer, then G has an Euler circuit.

https://math.berkeley.edu/~arash/55/10_5.pdf

https://courses.engr.illinois.edu/cs173/su2014/Lectures/Euler.pdf

1 vote

If a Graph G is Eulerian then all nodes will have Even degree But is the reverse True i.e. for any graph G’ if nodes of G’ have even degrees then G’ is Eulerian?

1

Yes.

If a simple graph G is connected and the degree of every vertex of G is a positive even integer, then G has an Euler circuit.

https://math.berkeley.edu/~arash/55/10_5.pdf

https://courses.engr.illinois.edu/cs173/su2014/Lectures/Euler.pdf